Show commands:
SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 163800.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163800.dd1 | 163800ew2 | \([0, 0, 0, -247308675, 1496344510750]\) | \(1936101054887046531846/905403781953125\) | \(782268867607500000000000\) | \([2]\) | \(31997952\) | \(3.5407\) | |
| 163800.dd2 | 163800ew1 | \([0, 0, 0, -12933675, 31266385750]\) | \(-553867390580563692/657061767578125\) | \(-283850683593750000000000\) | \([2]\) | \(15998976\) | \(3.1941\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 163800.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 163800.dd do not have complex multiplication.Modular form 163800.2.a.dd
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
